- Observed mean changes in LOD (pink wavy line) (from 1650 CE is are quite accurate values)
- Tidal friction influence (straight light blue dotted line) of 2.3 [ms/cy] [Stephenson, 1997, page 513]
- Optimized mean changes in LOD (black crosses), this is as per my
optimized function (using Simplex
method with one linear and one periodic term).

The mean Solar Day function is also incorporated in the Excel XLA file for archaeoastronomy and geodesy functions.

- Average mean changes in LOD (yellow straight line), is around 1.72 [ms/cy], using my own Simplex optimized function. This is within the value range (1.70+/-0.05 [ms/cy]) as provided in Stephenson ([1997], page 514)

Interesting to see that there looks to be a periodicy of around 1550 years (also mentioned by Stephenson ([1997], page 516), if people know such a cycle and have some proof due to an astronomical/geophysical process, let me know.

It could be this periodicy is caused by the splining methodology used (based on the ideas of Slutzky [1937]), but I doubt that.

Another reason for a spurious periodicy could be due to the sampling of only a limited amount of eclipses (Stephenson's pool of observations), but I think that that would not results in such a long term periodicy, because:

- I am thinking that the Nyquist-Shannon
theory
of sampling and low pass (anti-aliasing) filtering could be related
to this idea. If this low pass filtering does not happen at half the
Nyquist sampling frequency one could get spurious frequencies (f
_{sample}+/- f_{actual}) in the relating analysis.

- Assuming say an on average sampling of every 6 years an eclipse (pool of 400 observations over a period of 2300 years).
- to get a spurious periodicy of 1550 years in an analysis, an actual periodicy of some 5.98 or 6.02 years (1/1550 = 1/6 +/- 1/actual) must exist in the real LOD (which is not 'filtered out'). Such a natural(/actual) periodicy is not likely, IMHO.
- furthermore the splining in 5 knots would also not stimulate
such a long term periodicy over all knot
intervals (the spurious periodicy would even vary much more per knot
interval;
because the amount of observations varies greatly per knot interval).

- In the above I used a uniform distribution of the observation, while in actual live it are random observations, but still the large variation of observation per knot interval would not give such a visible uniform long term periodicy over all knot intervals.
- A test, if this periodicy is spurious, is by deliberately
changing
the number of observations (larger spacing between observations) and
see if the periodicy changes in duration. If it is spurious, the
periodicy must change according to the (1/spurious = 1/sample +/-
1/actual) formula.

- Observed mean DeltaT (pink line)
- DeltaT due to tidal friction influence (straight light blue dotted line) [Stephenson, 1997, page 513]
- Optimized mean DeltaT (black crosses), this is as per the
integral of
my change in LOD function

This mean DeltaT function is also incorporated in the Excel XLA file for archaeoastronomy and geodesy functions.

- The average mean DeltaT (yellow line) based on LOD change of around 1.7 [ms/cy] is also depicted

If you want to test the formula (one can use Excel XLA file), let me know.

Major content related changes: May 3, 2006